Nondispersive solutions to the L 2-critical Half-Wave Equation

We consider the focusing L ²-critical half-wave equation in one space dimension, $$i \partial_t u = D u - |u|^2 u$$ , where D denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold ${M_{*} > 0}$ such that all H ^1/2 solutions with ${\|u\|_{L^2} < M_*}$ extend globally in time, while solutions with ${\|u\|_{L^2} \geq M_*}$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass ${\|u_0\|_{L^2} = M_*}$ . More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy E ₀ > 0 and the linear momentum ${P_0 \in \mathbb{R}}$ . In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for L ²-critical nonlinear PDEs with nonlocal dispersion.     

Experimental evidence for excess entropy discontinuities in glass-forming solutions

Glass transition temperatures T(g) are investigated in aqueous binary and multi-component solutions consisting of citric acid, calcium nitrate (Ca(NO(3))(2)), malonic acid, raffinose, and ammonium bisulfate (NH(4)HSO(4)) using a differential scanning calorimeter. Based on measured glass transition temperatures of binary aqueous mixtures and fitted binary coefficients, the T(g) of multi-component systems can be predicted using mixing rules. However, the experimentally observed T(g) in multi-component solutions show considerable deviations from two theoretical approaches considered. The deviations from these predictions are explained in terms of the molar excess mixing entropy difference between the supercooled liquid and glassy state at T(g). The multi-component mixtures involve contributions to these excess mixing entropies that the mixing rules do not take into account.     

Self-consistent study of triaxial deformations: Application to the isotopes of Kr,Sr, Zr and Mo

Self-consistent mean-field calculations of deformation energy surfaces have been performed for more than 30 exotic isotopes of the Kr, Sr, Zr and Mo elements. Our calculations extend to the proton drip line. We investigate the triaxial stability of the deformed ground states in the deformation regions N ≈ 38 and N ≈ 60. The results are in good agreement with the observed trends.     

Molecular structure and fluorescence behaviour of a benzoquinone/porphyrin/benzoquinone sandwich-molecule

For the benzoquinone/porphyrin/benzoquinone sandwich-molecule 1 a highly symmetrical structure with parallel ring planes and interplanar distances of 342 pm was derived from X-ray analysis. 1 shows, in comparison to 2, a very strong quenching of fluorescence indicating intramolecular electron transfer.     

Analysis of a linearization heuristic for single-machine scheduling to maximize profit

We consider the problem of schedulingn jobs without preemption on a single machine to maximize total profit, where profit is given by a nonincreasing, concave separable function of job starting times. A heuristic is given in which jobs are sequenced optimally relative to a specific linear approximation of the profit, function. This heuristic always obtains at least 2/3 of the optimal profit, and examples exist where the heuristic obtains only 2/3 of the optimal profit. A large class of alternative linearizations is considrred and shown to give arbitrarily bad results. Work supported in part by NSF Grant ECS 82-05438 to the University of Pennsylvania and ONR Contract N00014-81-C-0302.